Alternative determinism principle for topological analysis of chaos

LEFRANC, Marc

Document type :

Article dans une revue scientifique

DOI :

10.1103/PhysRevE.74.035202

Title :

Alternative determinism principle for topological analysis of chaos

Author(s) :

LEFRANC, Marc [Auteur]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]

Journal title :

Physical Review E : Statistical, Nonlinear, and Soft Matter Physics

Pages :

035202(R)

Publisher :

American Physical Society

Publication date :

2006

ISSN :

1539-3755

English keyword(s) :

chaos
entropy
knots
topology
simplicial spaces

HAL domain(s) :

Science non linéaire [physics]/Dynamique Chaotique [nlin.CD]

English abstract : [en]

The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core ...
Show more >The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Non spécifiée

Popular science :

Non

Collections :

Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) - UMR 8523

Source :

Harvested from HAL

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http://arxiv.org/pdf/nlin.CD/0503006
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